In multi-antenna systems, for example cross-polar interference cancellation (XPIC) systems and multiple-input multiple-output (MIMO) systems, the receiver typically needs accurate knowledge of the propagation channel between the transmitter and receiver in order to be able to decode transmitted data without an excessive amount of errors. In systems where radio frequency (RF) signals received by different antennas are down-converted using independent oscillators, phase noise from the various oscillators distorts the received signals. In an attempt to reduce oscillator phase noise, present highly spectral efficient communication systems rely on local oscillators with low phase noise. Other highly spectral efficient communication systems rely on the use of a common down converting oscillator for multiple receivers.